Abstract
Let E be a second countable locally compact Hausdorff space and let L be a linear operator with domain D(L) and range R(L) in C0(E). Suppose that D(L) is dense in E. The following assertions are equivalent:
-
(a)
For L the martingale problem is uniquely solvable and L is maximal for this property
-
(b)
The operator L generates a Feller semigroup in C0(E).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Bauer, Probability theory and elements of measure theory, Holt, Rinehart and Winston Inc., New York 1972.
R.M. Blumenthal and R.K. Getoor, Markov processes and potential theory, Pure and Applied mathematics 29: a series of monographs and textbooks, Academic Press, New York 1986.
R. Durrett, Brownian motion and martingales in analysis, Wadsworth, Advanced Books and Software, Belmont 1984.
S.N. Ethier and T.G. Kurtz, Markov processes, characterization and convergence, Wiley Series in Probability and Statistics, John Wiley and Sons, New York 1985.
N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes second edition, North-Holland, Amsterdam 1989.
T.M. Liggett, Interacting particle systems, Die Grundlehren der Mathematischen Wissenschaften 276, Springer Verlag, New York 1985.
D.W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes, Springer Verlag, Berlin 1979.
J.A. van Casteren, Generators of strongly continuous semigroups, Research Notes in Mathematics 115, Pitman, London 1985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Casteren, J.A. On martingales and feller semigroups. Results. Math. 21, 274–288 (1992). https://doi.org/10.1007/BF03323085
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03323085